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/*
 *    GeoTools - The Open Source Java GIS Toolkit
 *    http://geotools.org
 *
 *    (C) 2011, Open Source Geospatial Foundation (OSGeo)
 *    (C) 2003-2005, Open Geospatial Consortium Inc.
 *
 *    All Rights Reserved. http://www.opengis.org/legal/
 */
package org.opengis.geometry.coordinate;

import static org.opengis.annotation.Obligation.*;
import static org.opengis.annotation.Specification.*;

import java.util.List;
import org.opengis.annotation.UML;
import org.opengis.geometry.primitive.CurveInterpolation;

/**
 * A polynimal spline. An "n^th degree" polynomial spline shall be defined
 * piecewise as an n-degree polynomial, with up to C^n-1 continuity
 * at the control points where the defining polynomial changes. This level of continuity is
 * controlled by the attribute {@link #getNumDerivativesInterior numDerivativesInterior}. Parameters
 * shall include directions for as many as degree - 2 derivatives of the polynomial at the start and
 * end point of the segment. {@link LineString} is equivalent to a 1^st degree polynomial
 * spline. It has simple continuity at the {@linkplain #getControlPoints control points}
 * (C0), but does not require derivative information (degree - 2 = -1).
 *
 * NOTE: The major difference between the polynomial splines and the b-splines (basis splines) is
 * that polynomial splines pass through their control points, making the control point and sample
 * point array identical.
 *
 * @version ISO 19107
 * @author Martin Desruisseaux (IRD)
 * @since GeoAPI 2.0
 */
@UML(identifier = "GM_PolynomialSpline", specification = ISO_19107)
public interface PolynomialSpline extends SplineCurve {
    /**
     * The interpolation mechanism for a {@code PolynomialSpline} is {@link
     * CurveInterpolation#POLYNOMIAL_SPLINE POLYNOMIAL_SPLINE}.
     */
    @UML(identifier = "interpolation", obligation = MANDATORY, specification = ISO_19107)
    CurveInterpolation getInterpolation();

    /**
     * The values used for the initial derivative (up to {@linkplain #getDegree degree} - 2) used
     * for interpolation in this {@code PolynomialSpline} at the start point of the spline.
     *
     * 
The {@linkplain List#size size} of the returned list is 
     * ({@linkplain #getDegree degree} - 2).
     */
    @UML(identifier = "vectorAtStart", obligation = MANDATORY, specification = ISO_19107)
    List /*double[]*/ getVectorAtStart();

    /**
     * The values used for the final derivative (up to {@linkplain #getDegree degree} - 2) used for
     * interpolation in this {@code PolynomialSpline} at the end point of the spline.
     *
     * The {@linkplain List#size size} of the returned list is 
     * ({@linkplain #getDegree degree} - 2).
     */
    @UML(identifier = "vectorAtEnd", obligation = MANDATORY, specification = ISO_19107)
    List /*double[]*/ getVectorAtEnd();
}